The following side lengths, in meters, were given to a carpenter to build a front porch with a triangular design. The carpenter needs to determine with set of lengths will make a triangle to be able to use it in his design.
Option 1: side lengths: 3,3,6
Option 2: side lengths: 6,8,10
Option 3: side lengths: 4,6,13
To determine which set of side lengths will form a triangle, we have to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
For option 1: side lengths 3, 3, 6
3 + 3 = 6, which is equal to the third side length. This does not satisfy the triangle inequality theorem, so option 1 does not form a triangle.
For option 2: side lengths 6, 8, 10
6 + 8 = 14, which is greater than the third side length of 10. This satisfies the triangle inequality theorem, so option 2 forms a triangle.
For option 3: side lengths 4, 6, 13
4 + 6 = 10, which is less than the third side length of 13. This does not satisfy the triangle inequality theorem, so option 3 does not form a triangle.
Therefore, only option 2 with side lengths 6, 8, and 10 will form a triangle.